Tomato
Low parsley fills the open ground under staked tomatoes without crowding them, and any plant left to flower opens flat umbels that feed hoverflies and tiny parasitic wasps — the insects that work over tomato aphids and hornworm eggs.
Asparagus
Asparagus crowns feed from deep, permanent roots while parsley works the top 8 inches with its taproot, so the two share the bed without fighting over water. Parsley also covers bare soil between crowns while the spears are still short.
Chives
The onion scent of chives can help hide young parsley from carrot fly, which finds carrot-family plants by smell. Treat it as a small edge, not a substitute for fine insect mesh over the row.
Carrot
Gardeners have long paired these carrot-family relatives, and they do want the same deep, loose, evenly moist soil. No mechanism is demonstrated, and both attract carrot fly — so if you grow them side by side, mesh the whole planting as one.
Rose
Parsley is said to keep aphids off roses, a pairing that has circulated on companion charts for a century without supporting trials. It does make a tidy, harvestable edging at the foot of a rose, so the risk of trying it is small.